John Baez

Topology Seminar, University of Oxford, February 23, 2014 and

Operads and the Tree of Life

Trees are not just combinatorial structures: they are also biological
structures, both in the obvious way but also in the study of
evolution. Starting from DNA samples from living species, biologists
use increasingly sophisticated mathematical techniques to reconstruct
the most likely 'phylogenetic tree' describing how these species
evolved from earlier ones. In their work on this subject, they have
encountered an interesting example of an operad, which is obtained by
applying a variant of the Boardmann–Vogt 'W construction' to the
operad for commutative monoids. The operations in this operad are
labelled trees of a certain sort, and it plays a universal role in the
study of stochastic processes that involve branching. It also shows
up in tropical algebra. This talk is based on work in progress with
Nina Otter.